Okay, I know it's late and that the (cinematic) universe has taken a liking in Richard White and saved him from the misery ... by removing his entire existence forever... but I will still follow up on that. The character, within the context of the Richard Donner/Bryan Singer timeline is a brilliant addition. Not only does he serve as an excellent foil to Clark Kent/Superman, but to me in the end he serves the role of Jonathan Kent for Kal-El's son.
If they had made a sequel I don't think he would have turned hostile. The character was meant to be very positive and endearing, to turn him into an envious super-villain (I'm looking at you Harry Osborne) would be too simple. Richard is a respectable guy despite the fact that Clark would initially be jealous of him for 'leading the life that should have been mine'. By the end of the film, this role is reversed and it's Superman who now has what Richard had 'the life that should have been mine'. But he still manages to retain his family and Superman's son, he isn't a villain at all but the normal human being who must level with Superman in what might be the most important thing in his life: his family. Fact that he retains his goodwill would be truer to who he is. That wouldn't be 'pulling a Cyclops', it would be 'pulling an Wolverine' (remember X2?)
On the flip side, I think the hostility would come from Clark's side. By the end of the first film we left Kal-El content that he is no longer the last survivor of Krypton - he is no longer alone but has found Jason. This whole idea is threatened by the fact that despite that he can never be a part of Jason's life, at least not without being Clark Kent (a false persona). Would the Man of Tomorrow be the jealous father instead?
It has been speculated by most fans that the whole dilemma regarding Jason's parentage would be a long, unofficial custody battle between Richard and Kal-El. If this indeed drives the central conflict of the story, I think the only way it would end is with Lois breaking up with Richard and keeping her distance from Superman and taking the child to raise herself. Single-parent Lane is much more believable than the Lois we saw in the first film. So where does this leave Richard White? Why, as the guy who aids Superman in stopping the big bad villain of course! Even if we ignore the fact that Richard White is every bit the 90s Pete Ross, there's his status of being a White, the Harvey Dent to Kal's Bruce Wayne. But I didn't have to make that analogy, it was screaming that in the first film already. For variation, we could think of him as the reporter who seeks to oust Superman as Clark Kent (Lois probably figured this out later on?), leading to an antagonistic relationship with the Man of Tomorrow, but it wouldn't succumb to villainy. The greater question, in my opinion, is what will happen to the kid.
